Cube Root Calculator

This cube root calculator can easily find out the cube root of any number within a fraction of a second. Just enter the number to calculate the cube root.

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Cube rooting, or getting the cube root, is the inverse of cubing a number. The cube root of a number ‘x’ is the number that produces ‘x’ when cubed. This is also true in algebra for a quantity or an expression.

For example, the cube root of 27 is 3 as 33 = 27 (3 x 3 x 3). This can be represented using a cube root notation 327 = 3.

If you don’t want to use the cube root sign, the cube root can also be represented using the fraction 1/3 as an exponent.

So not the cube root of 27 can be represented as, 271/3 = 3.

The square root of negative values is positive, as we saw in the square root calculator. However, the situation is not the same when looking for the cube root or a negative value. The negative number’s cube root is also negative.

For example, the cube root of -27 will be -3.

You can always use our cube root calculator to calculate the cube root of negative as well as positive numbers within fraction of seconds.

Calculator Use

  • To compute the cube root of a number, simply input the value in the first field, and the calculator will immediately display the cube root value in the second field.

Cube Root Formula

The formula to calculate the cube root of a number is mentioned below.

cube root calculator formula

How to Find the Cube Root Without Using a Scientific Calculator

Until now, you would have calculated the cube root of the number with scientific calculators or online cube root calculators. But, what if you’re trapped in a circumstance where you don’t have access to a scientific calculator and only have a basic calculator on your phone and you need to find the cube root of a number? Don’t be daunted by the concept; we’re always here to assist you.

We will demonstrate a simple way for calculating the cube root of any number without the use of a scientific calculator. Yes, you read that correctly: at the end of this post, you will be able to compute the cube root of any number by hand.

This is not a novel method. This method has already been covered in the square root calculator. Take a look if you haven’t already.

Explaination with Example

This method is all about guess. For example, lets say you want to find out the cube root of 643. You know that 512 is the perfect cube with its cube root 8 (8 x 8 x 8 = 512) and the cube root of 729 is 9 (9 x 9 x 9 = 729). So logically the cube root of 643 must lie in between 8 and 9.

So let’s start multiplying the numbers between them one by one till we arrive at the answer. However, because we are dealing with decimals, we may need to round off the answer if we cannot get an exact figure.

1st guess is 8.5 (always select the middle value between 2 known integers). So cubing 8.5 we get 614.125 (8.5 x 8.5 x 8.5). So 8.5 is not the cube root of 643, but we are heading towards the exact value of the cube root. Now we know that the cube root of 643 lies between 8.5 and 9. So lets continue with our guessing method till we reach the exact answer.

2nd guess is 8.6, 8.6 x 8.6 x 8.6 = 636.056.
3rd guess is 8.7, 8.7 x 8.7 x 8.7 = 658.503.

As you can see we have almost reached near the exact value. So now we know that the cube root value of 643 lies in between 8.6 and 8.7. So, let’s keep going with the above procedure.

4th guess is 8.65, 8.65 x 8.65 x 8.65 = 647.214625.
5th guess is 8.63, 8.63 x 8.63 x 8.63 = 642.735647.
6th guess is 8.64, 8.64 x 8.64 x 8.64 = 644.972544.

Now we have much closer values than previous ones. Now we surely know that the cube root value of 643 is between 8.63 and 6.64.

7th guess is 8.631, 8.631 x 8.631 x 8.631 = 642.959104.
8th guess is 8.632, 8.632 x 8.632 x 8.632 = 643.182612.

We’ve almost arrived at the sweet spot. Although our eighth guess is very accurate, we still want to remove the decimals and find the exact number. So let’s take another shot at it.

9th guess is 8.6312, 8.6312 x 8.6312 x 8.632 = 643.003801 ≈ 643

Finally, we found 643’s cube root, which is 8.6312. We understand that this was a very time-consuming and stressful method, but it is what it is. Because of this, most of you will choose to use our cube root calculator, which is fine, but knowing how to find the cube root of a number is always useful.